| Banach空间中广义混合变分不等式解的迭代算法 |
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| 引用本文： | 李艳,夏福全.Banach空间中广义混合变分不等式解的迭代算法[J].四川师范大学学报(自然科学版),2011,34(1):13-19. |
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| 作者姓名： | 李艳 夏福全 |
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| 作者单位： | 1. 成都信息工程学院数学学院,四川,成都,610225
2. 四川师范大学数学与软件科学学院,四川,成都,610066 |
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| 基金项目： | 四川省教育厅自然科学青年基金(07ZB068)资助项目; 成都信息工程学院基金(CRF201006)对本文给予了资助 |
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| 摘 要： | 利用R.s.Burachik和S.Scheimberg(SIAM J control Optim,2001,39(5):1633-1649.)介绍的近似点算法和Bregman泛函,在自反Banach空间中建立了一类广义混合变分不等式解的迭代算法,证明了迭代序列是有定义的,并且弱收敛于广义混合变分不等式的解.同时,给出了...
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| 关 键 词： | 迭代算法 近似点算法 Bregman距离 仿单调算子 伪单调算子 |
Iterative Algorithm for Solving Generalized Mixed Variational Inequalities in Banach Spaces |
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| LI Yan,XIA Fu-quan.Iterative Algorithm for Solving Generalized Mixed Variational Inequalities in Banach Spaces[J].Journal of Sichuan Normal University(Natural Science),2011,34(1):13-19. |
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| Authors: | LI Yan XIA Fu-quan |
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| Affiliation: | LI Yan1,XIA Fu-quan2(1.College of Mathematics,Chengdu University of Information Technology,Chengdu 610225,Sichuan,2.College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan) |
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| Abstract: | By using the proximal point method introduced by Burachik and Scheimberg(SIAM J Control Optim,2001,39(5):1633-1649.) and the Bregman function,we construct an iterative algorithm for finding the approximate solutions of a class of generalized mixed variational inequalities in reflexive Banach spaces.We prove that the sequence of approximate solutions is well-defined and converges weakly to the exact solution of the generalized mixed variational inequality.We also give a sufficient and necessary condition for... |
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| Keywords: | Iterative schemes proximal point algorithm Bregman distance paramonotone operator pseudomonotone operator |
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